Best 1208 quotes in «math quotes» category

The shortest path between two truths in the real domain passes through the complex domain.

The skylines lit up at dead of night, the air-conditioning systems cooling empty hotels in the desert and artificial light in the middle of the day all have something both demented and admirable about them. The mindless luxury of a rich civilization, and yet of a civilization perhaps as scared to see the lights go out as was the hunter in his primitive night.

The so-called Pythagoreans, who were the first to take up mathematics, not only advanced this subject, but saturated with it, they fancied that the principles of mathematics were the principles of all things.

The study of mathematics is apt to commence in disappointment.

The student of mathematics must get rid of all arbitrary thinking and follow purely the demands of thought. In thinking in this way, the laws of the spiritual world flow into him. This regulated thinking leads to the most spiritual truths.

The sole cause of man's unhappiness is that he does not know how to stay quietly in his room.

The study of infinity is much more than a dry academic game. The intellectual pursuit of the absolute infinity is, as Georg Cantor realized, a form of the soul's quest for God. Whether or not the goal is ever reached, an awareness of the process brings enlightenment.

The testament of science is so continually in a flux that the heresy of yesterday is the gospel of today and the fundamentalism of tomorrow.

The Theory of Groups is a branch of mathematics in which one does something to something and then compares the result with the result obtained from doing the same thing to something else, or something else to the same thing.

The tantalizing and compelling pursuit of mathematical problems offers mental absorption, peace of mind amid endless challenges, repose in activity, battle without conflict, refuge from the goading urgency of contingent happenings, and the sort of beauty changeless mountains present to senses tried by the present day kaleidoscope of events.

The toughest thing for a homeschooler is the same as for a school teacher - shifting from a weak tea vision of math being grinding calculations to a rich frothy mug of math as an active way of thinking.

The supreme function of reason is to show man that some things are beyond reason.

The surprising thing about this paper is that a man who could write it would.

The Tour (de France) is essentially a math problem, a 2,000-mile race over three weeks that's sometimes won by a margin of a minute or less. How do you propel yourself through space on a bicycle, sometimes steeply uphill, at a speed sustainable for three weeks? Every second counts.

The theory of numbers is particularly liable to the accusation that some of its problems are the wrong sort of questions to ask. I do not myself think the danger is serious; either a reasonable amount of concentration leads to new ideas or methods of obvious interest, or else one just leaves the problem alone. "Perfect numbers" certainly never did any good, but then they never did any particular harm.

The ultimate act of cowardice is the fat-headed wrestling guy sitting behind the frail kid in math class, clipping him on the ear, saying: 'What are you going to do about that, faggot?' That is cowardice. When the bullets start flying past that jock's saucer-shaped ears, that's not cowardice. That's payback.

The trouble with facts is that there are so many of them.

The union of the mathematician with the poet, fervor with measure, passion with correctness, this surely is the ideal.

The U.S. ranks 25th in math and 21st in science. We are woefully behind. The only way to change this situation is through public-private partnerships.

The value of a problem is not so much coming up with the answer as in the ideas and attempted ideas it forces on the would be solver.

The whole of mathematics consists in the organization of a series of aids to the imagination in the process of reasoning.

The trouble with integers is that we have examined only the very small ones. Maybe all the exciting stuff happens at really big numbers, ones we can't even begin to think about in any very definite way. Our brains have evolved to get us out of the rain, find where the berries are, and keep us from getting killed. Our brains did not evolve to help us grasp really large numbers or to look at things in a hundred thousand dimensions.

The ways in which acquired savants show up are usually the same ways that congenital, or non-acquired, savant syndrome shows up. They tend to show up in the same areas: music, art, math, visual, spatial skills, and calendar calculating, although calendar calculating probably isn't quite as prominent in that group. They tend to show up quite quickly, or sort of explode on the scene and they then tend to have an obsessive sort of forceful quality about them in the same way as savant skills. So they tend to show up in the same ways.

The will of man is by his reason swayed.

Those who write against vanity want the glory of having written well, and their readers the glory of reading well, and I who write this have the same desire, as perhaps those who read this have also.

They look at what's more important, like subjects to help with the SAT's, etc. They miss that music is vital. It offers a break from a stressful day of science and math and it's different.

Though the structures and patterns of mathematics reflect the structure of, and resonate in, the human mind every bit as much as do the structures and patterns of music, human beings have developed no mathematical equivalent to a pair of ears. Mathematics can only be "seen" with the "eyes of the mind". It is as if we had no sense of hearing, so that only someone able to sight read music would be able to appreciate its patterns and harmonies.

This much I'm sure of. Chances for winning = 1 - (# of math students playing)/ (# of math students cheering). That's a fraction.

Thus, be it understood, to demonstrate a theorem, it is neither necessary nor even advantageous to know what it means. The geometer might be replaced by the "logic piano" imagined by Stanley Jevons; or, if you choose, a machine might be imagined where the assumptions were put in at one end, while the theorems came out at the other, like the legendary Chicago machine where the pigs go in alive and come out transformed into hams and sausages. No more than these machines need the mathematician know what he does.

Throughout the 1960s and 1970s devoted Beckett readers greeted each successively shorter volume from the master with a mixture of awe and apprehensiveness; it was like watching a great mathematician wielding an infinitesimal calculus, his equations approaching nearer and still nearer to the null point.

Thus, in a sense, mathematics has been most advanced by those who distinguished themselves by intuition rather than by rigorous proofs.

Time was when all the parts of the subject were dissevered, when algebra, geometry, and arithmetic either lived apart or kept up cold relations of acquaintance confined to occasional calls upon one another; but that is now at an end; they are drawn together and are constantly becoming more and more intimately related and connected by a thousand fresh ties, and we may confidently look forward to a time when they shall form but one body with one soul.

[The works of Archimedes] are without exception, monuments of mathematical exposition; the gradual revelation of the plan of attack, the masterly ordering of the propositions, the stern elimination of everything not immediately relevant to the purpose, the finish of the whole, are so impressive in their perfection as to create a feeling akin to awe in the mind of the reader.

To arrive at the simplest truth, as Newton knew and practiced, requires years of contemplation. Not activity Not reasoning. Not calculating. Not busy behaviour of any kind. Not reading. Not talking. Not making an effort. Not thinking. Simply bearing in mind what it is one needs to know.

To be a scholar of mathematics you must be born with talent, insight, concentration, taste, luck, drive and the ability to visualize and guess.

Today I said to the calculus students, "I know, you're looking at this series and you don't see what I'm warning you about. You look and it and you think, 'I trust this series. I would take candy from this series. I would get in a car with this series.' But I'm going to warn you, this series is out to get you. Always remember: The harmonic series diverges. Never forget it.

To be sure, mathematics can be extended to any branch of knowledge, including economics, provided the concepts are so clearly defined as to permit accurate symbolic representation. That is only another way of saying that in some branches of discourse it is desirable to know what you are talking about.

Today, it is not only that our kings do not know mathematics, but our philosophers do not know mathematics and - to go a step further - our mathematicians do not know mathematics.

Today, over half of China's undergraduate degrees are in math, science technology and engineering, yet only 16 percent of America's undergraduates pursue these schools.

To do mathematics is to engage in an act of discovery and conjecture, intuition and inspiration; to be in a state of confusion − not because it makes no sense to you, but because you gave it sense and you still don't understand what your creation is up to.

To isolate mathematics from the practical demands of the sciences is to invite the sterility of a cow shut away from the bulls.

To the wise, life is a problem; to the fool, a solution.

To think I have spent my life on absolute muck.

To the pure geometer the radius of curvature is an incidental characteristic - like the grin of the Cheshire cat. To the physicist it is an indispensable characteristic. It would be going too far to say that to the physicist the cat is merely incidental to the grin. Physics is concerned with interrelatedness such as the interrelatedness of cats and grins. In this case the "cat without a grin" and the "grin without a cat" are equally set aside as purely mathematical phantasies.

To think deeply of simple things.

...to characterize the import of pure geometry, we might use the standard form of a movie-disclaimer: No portrayal of the characteristics of geometrical figures or of the spatial properties of relationships of actual bodies is intended, and any similarities between the primitive concepts and their customary geometrical connotations are purely coincidental.

Today, more than ever before, science holds the key to our survival as a planet and our security and prosperity as a nation. It's time we once again put science at the top of our agenda and work to restore America's place as the world leader in science and technology.

To deny, to believe, and to doubt well, are to a man what the race is to a horse.

To divide a cube into two other cubes, a fourth power, or in general any power whatever into two powers of the same denomination above the second is impossible, and I have assuredly found an admirable proof of this, but the margin is too narrow to contain it.

To speak algebraically, Mr. M. is execrable, but Mr. G. is (x + 1)- ecrable.